Does my DSL modem need to be replaced?

My DSL modem is probably about 7 years old (that's a guess) and it runs well with the two computers that are connected to it through the actual Internet cords (the Internet is sorta sluggish but the main problem is the computers are also old and cluttered which contributes to other slowness… )
Anyway, the problem isn't the computers Internet, it's the wireless Internet. I use the Wi-Fi for my iPhone and it works well the majority of the day but maybe once or twice per day the Wi-Fi either shows up on my phone and says "unable to connect to this network" or shows up as connected but doesn't load anything… I would blame my phone, but it also does this on the wii, the Xbox, and other peoples wireless devices in my family. I've found that by turning the modem off and unplugging the wireless router for a minute or so solves the problem… Temporarily. Until the next day when it repeats itself.
My phone will sometimes show the three bars for a strong wireless connection and not actually be connected but the Internet on the computer will work fine… I've called AT&T about this and tried to explain to them how the signal shows up fine and appears to work, but isn't actually working and they say the only solution is to buy a new modem (obviously they would love to get $100 from us). I just feel there might be other cheaper solutions to this problem?
Does anyone know why the modem is doing this? Is it because it is old and needs to be replaced?

Yeah the equipment wears out after time. You should get a new one… It'll have a better transmitter anyways

The internet provider NOR the modem/router has anything to do with it. Wireless home networks are ALWAYS poor compared to a wired connection. Ductwork, plumbing, house wiring, appliances, even wireless phones can have an adverse effect on a wireless home network. Make sure your router/modem is centrally located in the house, if you live in a 2 story, set it high up in a 1st floor room.
Edit: and NO, new wireless modems or routers do NOT have a better signal! The signal by FCC law can only be so strong and you're liable to find your reception WILL be worse especially if the new modem/router has an internal antenna. I DESIGN Wi-Fi equipment little timmy boy. Stick in a category you might know something about! Explain to me where you got the inane notion an electronic device with no moving parts wears out?

If you have DSL you probably have an all in one modem/router. If that is the case, then it may be the problem it may not. It COULD be your wireless cards, I had one that went bad and would drop signals every 3 hours or so. Once I replaced the wireless card, it worked fine!

If you are connecting a modem to a router, then the router is more than likely the culprit.

A good way to figure this out is to get someone else wireless adapter and use it for a while, if it works great, then you know the problem is the router or modem. If it's still dropping signal after a short period of time then it's probably the wireless adapter. If you think it's the router, then try using someone elses for a while and see if that works… Then do the same with the modem (this may be pretty hard to do as every company provides their own modems and property software to use them).

There are a few things you could try to fix your problem though. The best solution is to change the wireless channel and see if that works. If that doesn't work, if you have cordless phones, move them away from the router, if that doesn't work… Well then you could try downgrading (going from WPA to WEP) or turning off your encryption completely (there's a low chance of success of this working).

If you simply can't get it working SEE if they can send a technician out to test the modem.